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4=x2+7x-22
We move all terms to the left:
4-(x2+7x-22)=0
We add all the numbers together, and all the variables
-(+x^2+7x-22)+4=0
We get rid of parentheses
-x^2-7x+22+4=0
We add all the numbers together, and all the variables
-1x^2-7x+26=0
a = -1; b = -7; c = +26;
Δ = b2-4ac
Δ = -72-4·(-1)·26
Δ = 153
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3\sqrt{17}}{2*-1}=\frac{7-3\sqrt{17}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3\sqrt{17}}{2*-1}=\frac{7+3\sqrt{17}}{-2} $
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